The figure shows a spring fixed at the bottom end of an incline of inclination 53° . A small block of mass 1 kg starts slipping down the incline from a point 9.5 m away from the free end of the spring. The block compresses the spring by 50 cm, stops momentarily and then rebounds through a distance of 5 m (from maximum deformed state of spring) up along the incline. If the value of friction coefficient is (4/x), then find the value of x.

Question

The figure shows a spring fixed at the bottom end of an incline of inclination 53° . A small block of mass 1 kg starts slipping down the incline from a point 9.5 m away from the free end of the spring. The block compresses the spring by 50 cm, stops momentarily and then rebounds through a distance of 5 m (from maximum deformed state of spring) up along the incline. If the value of friction coefficient is (4/x), then find the value of x. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Applying work-energy theorem, m g sin 53° × 5 =μ m g cos 53° × 15 ⇒ μ=(4/9)

Applying work-energy theorem, mgsin53∘×5 =μmgcos53∘×15 ⇒μ=94​

Applying work-energy theorem,
$m g sin 5 3^{\circ} \times 5$
$= μ m g cos 5 3^{\circ} \times 15$
$\Rightarrow μ = \frac{4}{9}$